$A$ copper voltameter is connected in series with a heater coil of resistance $0.1\,\Omega$. $A$ steady current flows in the circuit for $20$ minutes and a mass of $0.99\,g$ of copper is deposited at the cathode. If the electrochemical equivalent of copper is $0.00033\,g/C$, then the heat generated in the coil is ............... $J$.

Column-$I$ gives certain physical quantities associated with the flow of current through a metallic conductor. Column-$II$ gives some mathematical relations involving electrical quantities. Match Column-$I$ and Column-$II$ with appropriate relations.

$A$. Mobility	$P$. $\frac{m}{ne^2 \rho}$
$B$. Electrical conductivity	$Q$. $neAv_{d}$
$C$. Relaxation period	$R$. $\frac{v_{d}}{E}$
$D$. Current	$S$. $\frac{J}{E}$

Two different metals are joined end to end. One end is kept at a constant temperature and the other end is heated to a very high temperature. The graph depicting the thermo $e.m.f.$ $(E)$ versus temperature $(t)$ is:

Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the voltage $\Delta V$ developed between $B$ and $C$. The calculation is done in the following steps: $(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block. $(ii)$ Calculate the field $E(r)$ at distance $r$ from $A$ by using Ohm's law $E=\rho j$,where $j$ is the current per unit area at $r$. $(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$. $(iv)$ Repeat $(i), (ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$. $\Delta V$ measured between $B$ and $C$ is

$A$ battery of $emf$ $E$ and internal resistance $r$ is connected across a resistance $R$. Resistance $R$ can be adjusted to any value greater than or equal to zero. $A$ graph is plotted between the current $(i)$ passing through the resistance and potential difference $(V)$ across it. Select the correct alternative$(s)$.

$A$ cable consists of a copper wire of radius $9 \, mm$ having a resistance of $5 \, \Omega$. If this cable is replaced by $6$ copper wires each of radius $3 \, mm$,what will be the new resistance of the cable in $\Omega$?